Question

What are the solutions to 0=x^2-x+1?​

Answer 1

Answer: No solutions

Explanation:

There are no solutions to 0 = x² - x + 1.

[Method One]

We can solve this by rewriting the equation, but it is quicker to graph it when there are no solutions. See attached.

[Method Two]

I said we can solve this by solving an equation, here it is. We will use the quadratic formula since the equation given is already in the proper form.

`\displaystyle x=(-b\pm√(b^2-4ac) )/(2a)`

`\displaystyle x=(1\pm√((-1)^2-4(1)(1)) )/(2(1))`

`\displaystyle x=(1\pm√(-3) )/(2)`

-> Negative numbers don't have real square roots, so there is no solution